Decoding algebraic-geometric codes over elliptic curves when the number of errors exceeds half of the designed distance

V. M. Sidelnikov (1994) constructed decoding algorithms for Reed-Solomon codes when the number of errors exceeds half of the true minimum distance. We consider analogous methods for decoding algebraic-geometric codes over elliptic curves. If the number of errors t exceeds (d*-1)/2, where d* is the designed distance, the decoding problem is reduced to the problem of finding the common zeros of two polynomials, whose coefficients depend upon the known syndromes: O_t+1⁽⁰⁾ (Z₁,…,Z_r), O _t+1⁽¹⁾ (Z₁,…,Z_r) (we assume that variables Z_i take the values on a given affine elliptic curve X, and that r=2t-d*+2)